Modelling and Analysis of Thin-layer Drying Kinetics for Freeze-dried Carrot Slices

Abstract

This study investigated the influence of heating plate temperature on the thin-layer drying of carrot slices and identified the most supported mathematical model for predicting the drying kinetics. Experiments were conducted in a laboratory setup designed to mimic freeze-drying conditions. Carrot slices of thicknesses (2, 4 and 6 mm) were dried at temperatures (40, 50 and 60°C). The drying data obtained under these conditions were used to analyse moisture removal patterns and to determine the effective moisture diffusivity during the falling-rate period. To characterise the drying process, 5 semi-theoretical models (Page model, Modified Page model, Henderson model, Lewis/ Newton model, Logistic regression model) were fitted to the experiment. The suitability and predictive accuracy of each model were evaluated using statistical indicators, including the root mean square error (RMSE), coefficient of determination (R²) and reduced chi-square. All models showed acceptable performance. Among the models assessed, the logarithmic model consistently provided the best fit across the different temperature and thickness combinations. Its higher R² values and lower RMSE and chi-square values indicated a closer agreement between the predicted and observed drying behaviour for thin-layer drying of carrot slices under the tested conditions. The activation energy increased from 52.01 to 57.54 kJ/mol as slice thickness increased from 2 mm to 6 mm, indicating greater temperature sensitivity and higher energy demand for moisture removal in thicker slices. Similarly, the effective moisture diffusivity ranged from 4.86 × 10⁻¹¹ to 4.38 × 10⁻¹⁰ m²/s, confirming that slice thickness significantly affects moisture transfer during freeze-drying. These findings can support the optimisation of freeze-drying simulations and contribute to improving the design of drying systems for heat-sensitive foods.